This paper deals with the development of computationally efficient algorithms for 2-D finite-impulse response (FIR) Wiener filters and linear predictors which are optimum in the mean-square-error (MSE) sense. It turns out that the computational effort to determine the coefficients of the 2-D FIR restoration filter depends heavily on the statistical features of the input signal. It is shown that in the case of homogeneous signals, one can develop two very efficient algorithms which are, at least, 30-percent faster than other existing schemes. These algorithms are subsequently used for the efficient implementation of the introduced restoration techniques. Experimental results as well as performance evaluations of this technique are included.